Dini's theorem is a result in real analysis relating pointwise convergence of sequences of functions to uniform convergence on a closed interval.
For an increasing sequence 
of continuous functions
on an interval ![I=[a,b]](/images/equations/DinisTheorem/Inline2.svg)
which converges
pointwise on 
to a continuous function 
on 
,
Dini's theorem states that 
converges to 
uniformly on 
.
